When we go to Australia we go Premium Economy. The flight is too long to do economy and is made worse by being an evening flight which is when your body wants to sleep and it is not going to happen in economy class.
What I would suggest you do is sign up for VAustralia and Qantas email alerts for sales. For example, Qantas had a sale that ended last week that was selling PE seats for half price, so effectively you could buy two round trips in PE for $4000. Other sales I have seen is two PE seats for the price of one, $4000, but that only works if two of you are travelling together.
Personally I prefer the VAustralia product, the in flight service is better and the IFE is much better than Qantas as well. The only downside of using VAustralia is the frequent flyer aspect. I think base points on a PE fare to Oz is normally around 16k so you would want to be able to use these points in the future. Qantas flies out of SFO as well as LAX to Sydney, Melbourne and Brisbane. VAustralia only goes out of LAX to Brisbane and Sydney. Qantas does have a flight Sydney-Auckland-LAX if you wanted to incorporate NZ into your trip.
One other airline to consider is Air New Zealand as they go either SFO or LAX to Sydney via Auckland and they have a PE section as well. I have not flown with them but they have a good reputation. I have been looking for flights to Oz this week and ANZ have had the best prices. ANZ is part of the Star Alliance so if you are a member of the United Frequent Flyer program they may work the best for you.